#include <bits/stdc++.h> #include <atcoder/all> using namespace std; using ll = long long; using ul = unsigned long; using ld = long double; using st = string; using mint = atcoder::modint998244353; using Mint = atcoder::modint1000000007; #define vl vector<ll> #define vvl vector<vector<ll>> #define vvvl vector<vector<vector<ll>>> #define vvvvl vector<vector<vector<vector<ll>>>> #define vd vector<ld> #define vvd vector<vector<ld>> #define vvvd vector<vector<vector<ld>>> #define vb vector<bool> #define vvb vector<vector<bool>> #define vvvb vector<vector<vector<bool>>> #define vs vector<string> #define vvs vector<vector<string>> #define vvvs vector<vector<vector<string>>> #define vp vector<pair<ll,ll>> #define vvp vector<vector<pair<ll,ll>>> #define vvvp vector<vector<vector<pair<ll,ll>>>> #define vm vector<mint> #define vvm vector<vector<mint>> #define vM vector<Mint> #define vvM vector<vector<Mint>> #define cmx(n,v) n=n<v?v:n #define cmn(n,v) n=n>v?v:n #define all(n) begin(n),end(n) #define nxp(a) next_permutation(all(a)) #define rev(n) reverse(all(n)) #define sor(n) stable_sort(all(n)) #define rep(i,n) for(ll i=0;i<(n);++i) #define reprev(i,n) for(ll i=n-1;0<=i;--i) #define rrep(i,a,n) for(ll i=a;i<(n);++i) #define sz(n) n.size() #define bit(j,i) (i&(1<<j)) #define yn(x) cout << (x?"Yes":"No") << endl; #define lb(vec,src) lower_bound(vec.begin(),vec.end(),src)-vec.begin() #define ub(vec,src) upper_bound(vec.begin(),vec.end(),src)-vec.begin() #define lb2(vec,src) *lower_bound(vec.begin(),vec.end(),src) #define ub2(vec,src) *upper_bound(vec.begin(),vec.end(),src) #define mne1(a) min_element(all(a)) #define mxe1(a) max_element(all(a)) #define mne2(a) *min_element(all(a)) #define mxe2(a) *max_element(all(a)) #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} const ll inf = 9e18; ll calc_digit(ll N){ ll res = 0; while(N>0){ res++; N/=10; } return res; } ll factorial(ll n, ll mod = 1e18) { ll ans = 1; for(ll i = n; i >= 2; i--) ans = (ans * i) % mod; return ans; } ll round_up(ll x,ll y){ return (x+y-1)/y; } ll floor_int(ll x,ll m){ ll r=(x%m+m)%m; //負の剰余を正の剰余に置き換える return (x-r)/m; //return } ll rmd(ll x,ll m){ ll r=(x%m+m)%m; //負の剰余を正の剰余に置き換える return r; } ll rmd_2(ll x,ll m){ ll r=(x%m+m)%m; //負の剰余を正の剰余に置き換える return (m-r)%m; //return } ll bubble_sort(vl a,ll n){ ll res=0; rep(i,n-1){ for(ll j=n-1;j>i;j--){ if(a[j-1]>a[j]){ swap(a[j-1],a[j]); res++; } } } return res; } ll sum_v(vl a){ ll res=0; ll n=sz(a); rep(i,n) res+=a[i]; return res; } ll stair_sum(ll from,ll to){ return (from+to)*(to-from+1)/2; } ll Power(ll var, ll p) { if (p == 1) return var; ll ans = Power(var * var, p / 2); if (p & 1) ans *= var;; return ans; } ll cnt_01(ll n,ll now){ ll res=0; res+=(n/now)*(now/2); if(n%now>=now/2) res+=n%now-(now/2)+1; return res; } ll sum_pop(ll n){ ll res=0; for(ll b=0;b<60;b++){ res+=(n/(1ll<<(b+1)))*(1ll<<b); res+=max(0ll,n%(1ll<<(b+1))-(1ll<<b)+1); } return res; } ll Tree_Diameter(vvl& g){ ll n=sz(g); ll start=0; ll ans=0; for(ll i=0;i<2;i++){ queue<ll> q; q.push(start); vl dis(n,inf); dis[start]=0; while(!q.empty()){ ll u=q.front(); q.pop(); start=u; ans=dis[u]; for(ll v:g[u]){ if(dis[v]!=inf) continue; dis[v]=dis[u]+1; q.push(v); } } } return ans; } mint m_Power(mint var,ll p) { if (p == 1) return var; mint ans = m_Power(var * var, p / 2); if (p & 1) ans *= var;; return ans; } Mint M_Power(Mint var,ll p) { if (p == 1) return var; Mint ans = M_Power(var * var, p / 2); if (p & 1) ans *= var;; return ans; } bool is_prime(ll N){ if(N==1) return false; if(N==2) return true; if(N%2==0) return false; for(ll p=3;p*p<=N;p+=2) if(N%p==0) return false; return true; } bool in_out(ll x,ll y,ll h,ll w){ return 0<=x and x<h and 0<=y and y<w; } bool dis_solve1(ll x1,ll x2,ll y1,ll y2,ll r){ ll xx=(x1-x2),yy=(y1-y2); ll dis=xx*xx+yy*yy; return (r*r==dis); } bool dis_solve2(ll x1,ll x2,ll y1,ll y2,ll d1,ll d2){ ll xx=(x1-x2),yy=(y1-y2),r1=(d1+d2),r2=(d1-d2); ll dis=xx*xx+yy*yy; return (r2*r2<=dis&&dis<=r1*r1); } void printl(vl v,ll len=0){ ll vsz=min(len,ll(v.size())); for(ll i=0;i<vsz;i++){ cout << v[i] << endl; } } void prints(vs v){ ll vsz=v.size(); for(ll i=0;i<vsz;i++){ cout << v[i] << endl; } } vl p_list(ll n){ vl res; vb check(n+1); for(ll i=2;i<=n;i++){ if(check[i]) continue; res.push_back(i); ll ii=i; while(ii<=n){ check[ii]=true; ii+=i; } } return res; } vl cumulative_sum(vl a){ ll s=sz(a); vl b(s+1,0); for(ll i=0;i<s;i++){ b[i+1]=a[i]+b[i]; } return b; } vl n_num(ll a,ll n){ vl res; while(a){ res.push_back(a%n); a/=n; } rev(res); return res; } vl c_press(vl a){ ll n=sz(a); vl res=a,c=a; sor(c); uniq(c); rep(i,n) res[i]=lb(c,res[i]); return res; } vl min_fact(ll n){ vl pl; vl res(n+1,-1); for(ll d=2;d<=n;d++){ if(res[d]==-1){ res[d]=d; pl.push_back(d); } for(ll p:pl){ if(p*d>n||p>res[d]) break; res[p*d]=p; } } return res; } vvl to_grid(vl &a,ll k){ ll n=sz(a); ll m=(n+k-1)/k; vvl b(k,vl(m,inf)); rep(i,n) b[i%k][i/k]=a[i]; return b; } vvl rotate_ll(vvl& V2d,ll wise){ vvl a=V2d; ll h=sz(a),w=sz(a[0]); vvl res(w,vl(h)); if(wise) {rep(i,h)rep(j,w) res[j][h-i-1]=a[i][j];} else {rep(i,h)rep(j,w) res[w-j-1][i]=a[i][j];} return res; } vs rotate_st(vs s,ll wise){ vs a=s; ll h=sz(a),w=sz(a[0]); vs res(w); rep(i,w) res[i].append(h,'.'); if(wise) {rep(i,h)rep(j,w) res[j][h-i-1]=a[i][j];} else {rep(i,h)rep(j,w) res[w-j-1][i]=a[i][j];} return res; } vp prime_factorize(ll N){ vp res; for (ll a = 2; a * a <= N; ++a) { if (N % a != 0) continue; ll ex = 0; while (N % a == 0) { ex++; N /= a; } res.push_back({a, ex}); } if (N != 1) res.push_back({N, 1}); return res; } template <typename T> void input(T &a) { cin >> a; }; template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); }; template<typename T = ll> vector<T> rd(size_t n) { vector<T> ts(n); for (size_t i = 0; i < n; i++) cin >> ts[i]; return ts; } template<typename TV, const ll N> void read_tuple_impl(TV&) {} template<typename TV, const ll N, typename Head, typename... Tail> void read_tuple_impl(TV& ts) { get<N>(ts).emplace_back(*(istream_iterator<Head>(cin))); read_tuple_impl<TV, N + 1, Tail...>(ts); } template<typename... Ts> decltype(auto) read_tuple(size_t n) { tuple<vector<Ts>...> ts; for (size_t i = 0; i < n; i++) read_tuple_impl<decltype(ts), 0, Ts...>(ts); return ts; } ll di[8]={1,-1,0,0,1,1,-1,-1}; ll dj[8]={0,0,1,-1,1,-1,-1,1}; //abcdefghijklmnopqrstuvwxyz //std::setprecision(15); //2^29<10^9 int main(){ ios::sync_with_stdio(0); cin.tie(0); ll n; cin >> n; vl a=rd(n); vl cnt(3); rep(i,n){ if(a[i]>=3) continue; cnt[a[i]]++; } map<array<ll,3>,ld> dp; dp[{0,0,0}]=0.0; auto e = [&] (auto f,ll i,ll j,ll k) -> ld { if(dp.count({i,j,k})) return dp[{i,j,k}]; ld res=ld(n)/ld(i+j+k); if(i>0) res+=f(f,i-1,j+1,k)*(ld(i)/ld(i+j+k)); if(j>0) res+=f(f,i,j-1,k+1)*(ld(j)/ld(i+j+k)); if(k>0) res+=f(f,i,j,k-1)*(ld(k)/ld(i+j+k)); return dp[{i,j,k}]=res; }; ld ans=e(e,cnt[0],cnt[1],cnt[2]); cout << setprecision(15) << ans << endl; return 0; }